import numpy as np
import pandas as pd
from itertools import cycle
from scipy import interp

# sklearn
from sklearn import metrics
from sklearn.model_selection import train_test_split, StratifiedShuffleSplit
from sklearn import datasets
from sklearn.preprocessing import StandardScaler
from sklearn import preprocessing

# TensorFlow
import tensorflow as tf

# Timer
from timeit import default_timer as timer

# Visualisation libraries

## Text
from colorama import Fore, Back, Style
from IPython.display import Image, display, Markdown, Latex, clear_output

## progressbar
import progressbar

## plotly
from plotly.offline import init_notebook_mode, iplot 
import plotly.graph_objs as go
import plotly.offline as py
from plotly.subplots import make_subplots
import plotly.express as px

## seaborn
import seaborn as sns

## matplotlib
import matplotlib.pyplot as plt
from matplotlib.patches import Ellipse, Polygon
from matplotlib.font_manager import FontProperties
import matplotlib.colors as mcolors
from matplotlib import cm
plt.style.use('seaborn-whitegrid')
plt.rcParams['axes.labelsize'] = 14
plt.rcParams['xtick.labelsize'] = 12
plt.rcParams['ytick.labelsize'] = 12
plt.rcParams['text.color'] = 'k'
%matplotlib inline

import warnings
warnings.filterwarnings("ignore")

Home / Healthcare Analytics and Modeling

Heart Disease Dataset

• Exploratory Data Analysis
• Modeling: Tensorflow Linear Classifier
• Modeling: Tensorflow DNN Classifier
• Modeling: Tensorflow Boosted Trees Classifier
• Modeling: Tensorflow Boosted Trees Classifier with Feature Importance Analysis

Heart Disease Dataset

In this article, we demonstrate solving a classification problem in TensorFlow using Estimators using the Heart Disease Dataset from the UCI Machine Learning Repository.

Picture Source: harvard.edu

Attribute Information:

1. Age
2. Sex
   • 0: Female
   • 1: Male
3. Chest Pain Type
   • 1: Typical Angina
   • 2: Atypical Angina
   • 3: Non-Anginal Pain
   • 4: Asymptomatic

• Resting Blood Pressure

1. Serum Cholestoral (in mg/dl )
2. FBS: Fasting Blood Sugar > 120 mg/dl
   • 0 = False
   • 1 = True
3. Resting Electrocardiographic Results
   • 0: normal
   • 1: having ST-T wave abnormality (T wave inversions and/or ST elevation or depression of > 0.05 mV)
   • 2: showing probable or definite left ventricular hypertrophy by Estes' criteria
4. Maximum Heart Rate Achieved
5. Exercise Induced Angina
   • 0: No
   • 1: Yes
6. Oldpeak = St Depression Induced By Exercise Relative To Rest
7. Slope: The Slope Of The Peak Exercise ST Segment
   • 1: Upsloping
   • 2: Flat
   • 3: Downsloping
8. Number Of Major Vessels (0-3) Colored By Flourosopy
9. Thal
   • 3: Normal
   • 6: Fixed Defect
   • 7: Reversable Defect

Variable to be predicted

• Heart Disease
  • 0: Absence
  • 1: Presence

Problem Description

Developing a predictive model that can predict whether heart disease is present or absent based on the rest of the given features.

Data = np.genfromtxt('heart-disease/heart.dat', delimiter=' ')
Attributes = ['Age', 'Sex', 'Chest Pain Type', 'Resting Blood Pressure', 'Serum Cholestoral',
              'Fasting Blood Sugar', 'Resting Electrocardiographic Results', 'Maximum Heart Rate Achieved',
              'Exercise Induced Angina', 'Oldpeak', 'Slope',
              'Number of Major Vessels', 'Thal', 'Heart Disease']
Data = pd.DataFrame(data = Data, columns = Attributes)
# 
Temp = ['Sex', 'Chest Pain Type', 'Fasting Blood Sugar', 'Resting Electrocardiographic Results',
       'Exercise Induced Angina', 'Slope', 'Number of Major Vessels','Thal']
for c in Temp:
    Data[c] = Data[c].astype(int).astype(str)
del Temp, c
Target = 'Heart Disease'
Labels_dict = dict(zip([0,1],['Absent', 'Present']))
Data['Heart Disease'] = (Data['Heart Disease']-1).astype(int)
#
display(Data.head(5))
display(pd.DataFrame({'Number of Instances': [Data.shape[0]], 'Number of Attributes': [Data.shape[1]]}).style.hide_index())

# Maps
Maps = {'Sex': {'0':'Female', '1':'Male'},
        'Chest Pain Type': {'1':'Typical Angina', '2':'Atypical Angina', '3': 'Non-Anginal Pain', '4':'Asymptomatic'},
        'Fasting Blood Sugar': {'0': 'False', '1': 'True'}, 'Exercise Induced Angina': {'0': 'No', '1': 'Yes'},
        'Slope': {'1': 'Upsloping', '2': 'Flat', '3': 'Downsloping'},
        'Thal':  {'3': 'Normal', '6': 'Fixed Defect','7': 'Reversable Defect'}}

	Age	Sex	Chest Pain Type	Resting Blood Pressure	Serum Cholestoral	Fasting Blood Sugar	Resting Electrocardiographic Results	Maximum Heart Rate Achieved	Exercise Induced Angina	Oldpeak	Slope	Number of Major Vessels	Thal	Heart Disease
0	70.0	1	4	130.0	322.0	0	2	109.0	0	2.4	2	3	3	1
1	67.0	0	3	115.0	564.0	0	2	160.0	0	1.6	2	0	7	0
2	57.0	1	2	124.0	261.0	0	0	141.0	0	0.3	1	0	7	1
3	64.0	1	4	128.0	263.0	0	0	105.0	1	0.2	2	1	7	0
4	74.0	0	2	120.0	269.0	0	2	121.0	1	0.2	1	1	3	0

Number of Instances	Number of Attributes
270	14

def Data_Plot(Inp, Title = None, W = None):
    data_info = Inp.dtypes.astype(str).to_frame(name='Data Type')
    Temp = Inp.isnull().sum().to_frame(name = 'Number of NaN Values')
    data_info = data_info.join(Temp, how='outer')
    data_info ['Size'] = Inp.shape[0]
    data_info['Percentage'] = 100 - np.round(100*(data_info['Number of NaN Values']/Inp.shape[0]),2)
    data_info = data_info.reset_index(drop = False).rename(columns = {'index':'Features'})
    #
    fig = px.bar(data_info, x= 'Features', y= 'Percentage', color = 'Data Type',
                 text = 'Percentage',
                 color_discrete_sequence = ['PaleGreen', 'LightCyan', 'PeachPuff', 'Pink', 'Plum'],
                 hover_data = data_info.columns)
    fig.update_layout(plot_bgcolor= 'white', legend=dict(x=1.01, y=.5, traceorder="normal",
                                                         bordercolor="DarkGray", borderwidth=1))
    if not W == None:
        fig.update_layout(width = W)
    fig.update_traces(texttemplate= 10*' ' + '%%{text}', textposition='inside')
    fig.update_traces(marker_line_color= 'Black', marker_line_width=1., opacity=1)
    if not Title == None:
        fig.update_layout(title={'text': '<b>' + Title + '<b>', 'x':0.5,
                                         'y':0.90, 'xanchor': 'center', 'yanchor': 'top'})
    fig.show()
    return data_info

data_info = Data_Plot(Data, Title = 'Heart Disease Dataset', W = 800)

X and y sets

# A copy of the Dataframe
df = Data.copy()
# for TF
df.columns = [x.replace(' ','_') for x in df.columns] 
Temp = Target.replace(' ','_')
X = df.drop(columns = Temp)
y = df[Temp].values
del df, Temp

Train and Test sets

def DatasetTargetDist(Inp, Target, Labels_dict, PD):
    # Table
    Table = Inp[Target].value_counts().to_frame('Count').reset_index(drop = False).rename(columns = {'index':Target})
    Table[Target] = Table[Target].replace(Labels_dict)
    Table['Percentage'] = np.round(100*(Table['Count']/Table['Count'].sum()),2)
    fig = make_subplots(rows=1, cols=2, horizontal_spacing = 0.02, column_widths=PD['column_widths'],
                        specs=[[{"type": "table"},{"type": "pie"}]])

    # Right
    fig.add_trace(go.Pie(labels=Table[Target].values, values=Table['Count'].values,
                         pull=PD['pull'], textfont=dict(size= PD['textfont']),
                         marker=dict(colors = PD['PieColors'], line=dict(color='black', width=1))), row=1, col=2)
    fig.update_traces(hole=PD['hole'])
    fig.update_layout(height = PD['height'], legend=dict(orientation="v"), legend_title_text= PD['legend_title'])
    
    # Left
    T = Table.copy()
    T['Percentage'] = T['Percentage'].map(lambda x: '%%%.2f' % x)
    Temp = []
    for i in T.columns:
        Temp.append(T.loc[:,i].values)

    fig.add_trace(go.Table(header=dict(values = list(Table.columns), line_color='darkslategray',
                                       fill_color= PD['TableColors'][0], align=['center','center'],
                                       font=dict(color='white', size=12), height=25), columnwidth = PD['tablecolumnwidth'],
                           cells=dict(values=Temp, line_color='darkslategray',
                                      fill=dict(color= [PD['TableColors'][1], PD['TableColors'][1]]),
                                  align=['center', 'center'], font_size=12, height=20)), 1, 1)

    fig.update_layout(title={'text': '<b>' + Target + '<b>', 'x':PD['title_x'],
                                     'y':PD['title_y'], 'xanchor': 'center', 'yanchor': 'top'})
    fig.show()

Pull = [0 for x in range((len(Labels_dict)-1))]
Pull.append(.05)
PD = dict(PieColors = ['SeaGreen','FireBrick'],
          TableColors = ['Navy','White'], hole = .4,
          column_widths=[0.6, 0.4],textfont = 14, height = 350, tablecolumnwidth = [0.20, 0.12, 0.15],
          pull = Pull, legend_title = Target, title_x = 0.5, title_y = 0.8)
del Pull
DatasetTargetDist(Data, Target, Labels_dict, PD)

StratifiedKFold is a variation of k-fold which returns stratified folds: each set contains approximately the same percentage of samples of each target class as the complete set.

Test_Size = 0.3
sss = StratifiedShuffleSplit(n_splits=1, test_size=Test_Size, random_state=42)
_ = sss.get_n_splits(X, y)
# For Tensorflow
X.columns = [x.replace(' ','_') for x in X.columns]

for train_index, test_index in sss.split(X, y):
    # X
    if isinstance(X, pd.DataFrame):
        X_train, X_test = X.loc[train_index], X.loc[test_index]
    else:
        X_train, X_test = X[train_index], X[test_index]
    # y    
    if isinstance(y, pd.Series):
        y_train, y_test = y[train_index], y[test_index]
    else:
        y_train, y_test = y[train_index], y[test_index]
del sss

def Train_Test_Dist(X_train, y_train, X_test, y_test, PD, Labels_dict = Labels_dict):
    def ToSeries(x):
        if not isinstance(x, pd.Series):
            Out = pd.Series(x)
        else:
            Out = x.copy()
        return Out
    
    fig = make_subplots(rows=1, cols=3, horizontal_spacing = 0.02, column_widths= PD['column_widths'],
                        specs=[[{"type": "table"},{'type':'domain'}, {'type':'domain'}]])
    # Right
    C = 2
    for y in [ToSeries(y_train).replace(Labels_dict), ToSeries(y_test).replace(Labels_dict)]:
        fig.add_trace(go.Pie(labels= list(Labels_dict.values()),
                             values= y.value_counts().values, pull=PD['pull'],
                             textfont=dict(size=PD['textfont']),
                             marker=dict(colors = PD['PieColors'],
                             line=dict(color='black', width=1))), row=1, col=C)
        fig.update_traces(hole=.5)
        fig.update_layout(legend=dict(orientation="v"), legend_title_text= PD['legend_title'])
        C+=1
    
    # Left
    
    # Table
    Table = pd.DataFrame(data={'Set':['X_train','X_test','y_train','y_test'],
                       'Shape':[X_train.shape, X_test.shape, y_train.shape, y_test.shape]}).astype(str)
    T = Table.copy()
    Temp = []
    for i in T.columns:
        Temp.append(T.loc[:,i].values)
        
    TableColors = PD['TableColors']
    fig.add_trace(go.Table(header=dict(values = list(Table.columns), line_color='darkslategray',
                                       fill_color= TableColors[0], align=['center','center'],
                                       font=dict(color='white', size=12), height=25), columnwidth = PD['tablecolumnwidth'],
                           cells=dict(values=Temp, line_color='darkslategray',
                                      fill=dict(color= [TableColors[1], TableColors[1]]),
                                  align=['center', 'center'], font_size=12, height=20)), 1, 1)
    fig.update_layout(title={'text': '<b>' + 'Dataset Distribution' + '<b>', 'x':PD['title_x'],
                                     'y':PD['title_y'], 'xanchor': 'center', 'yanchor': 'top'})
    if not PD['height'] == None:
        fig.update_layout(height = PD['height'])
    fig.show()
    
PD.update(dict(column_widths=[0.3, 0.3, 0.3], tablecolumnwidth = [0.2, 0.4], height = 350, legend_title = Target))

Train_Test_Dist(X_train, y_train, X_test, y_test, PD)

Input Function

The input function specifies how data is converted to a tf.data.Dataset that feeds the input pipeline in a streaming fashion. Moreover, an input function is a function that returns a tf.data.Dataset object which outputs the following two-element tuple:

• features - A Python dictionary in which:
  • Each key is the name of a feature.
  • Each value is an array containing all of that feature's values.
• label - An array containing the values of the label for every example.

def input_fn(features, labels, training=True, batch_size=256):
    """An input function for training or evaluating"""
    # Convert the inputs to a Dataset.
    dataset = tf.data.Dataset.from_tensor_slices((dict(features), labels))

    # Shuffle and repeat if you are in training mode.
    if training:
        dataset = dataset.shuffle(1000).repeat()
    
    return dataset.batch(batch_size)

Moreover, an estimator model consists of two main parts, feature columns, and a numeric vector. Feature columns provide explanations for the input numeric vector. The following function separates categorical and numerical columns (features)and returns a descriptive list of feature columns.

def Feat_Columns(Inp):
    Temp = Inp.dtypes.reset_index(drop = False)
    Temp.columns = ['Features', 'Data Type']
    Temp['Data Type'] = Temp['Data Type'].astype(str)
    # Numeric_Columns
    Numeric_Columns = Temp.loc[Temp['Data Type'].isin(['int64', 'int32', 'float64', 'float32']),'Features'].tolist()
    # Categorical_Columns
    Categorical_Columns = Temp.loc[Temp['Data Type'] == 'object','Features'].tolist()
        
    # Feature Columns
    feature_columns = []
    if len(Categorical_Columns)>0:
        for feature_name in Categorical_Columns:
          vocabulary = Inp[feature_name].unique()
          feature_columns.append(tf.feature_column.categorical_column_with_vocabulary_list(feature_name, vocabulary))
    if len(Numeric_Columns)>0:
        for feature_name in Numeric_Columns:
          feature_columns.append(tf.feature_column.numeric_column(feature_name))
    return feature_columns

my_feature_columns = Feat_Columns(X)

Modeling: Boosted Trees Classifier

tf.keras.backend.clear_session()
IT = int(5e3)
# Classifier
classifier = tf.estimator.BoostedTreesClassifier(feature_columns=my_feature_columns,
                                                 n_batches_per_layer= 1,
                                                 n_classes= len(Labels_dict),
                                                 learning_rate=0.1)
# Training
classifier.train(input_fn=lambda: input_fn(X_train, y_train, training=True), max_steps = IT)
result = classifier.evaluate(input_fn=lambda: input_fn(X_test, y_test, training=False))
clear_output()
display(pd.DataFrame(result, index = ['']).round(4))

	accuracy	accuracy_baseline	auc	auc_precision_recall	average_loss	label/mean	loss	precision	prediction/mean	recall	global_step
	0.8272	0.5556	0.8583	0.8505	1.5855	0.4444	1.5855	0.8056	0.44	0.8056	600

ROC Curves

def ROC_Curve(y_test, probs, n_classes, FS = 7, ax = False, pad = 0.01):
    # converting y_test to categorical
    y_test_cat = tf.keras.utils.to_categorical(y_test, num_classes=n_classes, dtype='float32')
    # Compute ROC curve and ROC area for each class
    fpr = dict()
    tpr = dict()
    roc_auc = dict()
    for i in range(n_classes):
        fpr[i], tpr[i], _ = metrics.roc_curve(y_test_cat[:, i], probs[:, i])
        roc_auc[i] = metrics.auc(fpr[i], tpr[i])

    # Compute micro-average ROC curve and ROC area
    fpr["micro"], tpr["micro"], _ = metrics.roc_curve(y_test_cat.ravel(), probs.ravel())
    roc_auc["micro"] = metrics.auc(fpr["micro"], tpr["micro"])

    # First aggregate all false positive rates
    all_fpr = np.unique(np.concatenate([fpr[i] for i in range(n_classes)]))

    # Then interpolate all ROC curves at this points
    mean_tpr = np.zeros_like(all_fpr)
    for i in range(n_classes):
        mean_tpr += interp(all_fpr, fpr[i], tpr[i])

    # Finally average it and compute AUC
    mean_tpr /= n_classes

    fpr["macro"] = all_fpr
    tpr["macro"] = mean_tpr
    roc_auc["macro"] = metrics.auc(fpr["macro"], tpr["macro"])

    fig = go.Figure()
    fig.add_trace(go.Scatter(x=[0, 1], y=[0, 1], name = 'FPR = TPR', line = dict(color='Black', width=2, dash='dash')))
    fig.add_trace(go.Scatter(x=fpr["micro"], y=tpr["micro"], mode='lines', marker_color = 'deeppink',
                             name='micro-average ROC curve (area = {0:0.2f})'.format(roc_auc["micro"])))
    fig.add_trace(go.Scatter(x=fpr["macro"], y=tpr["macro"], mode='lines', marker_color = 'navy',
                             name='macro-average ROC curve (area = {0:0.2f})'.format(roc_auc["macro"])))

    colors = cycle(['Aqua', 'DarkOrange', 'CornflowerBlue'])
    for i, color in zip(range(n_classes), colors):
        _ = fig.add_trace(go.Scatter(x = fpr[i], y = tpr[i], mode='lines', marker_color= px.colors.sequential.Rainbow,
                                     name='ROC curve of class {0} (area = {1:0.2f})'.format(i, roc_auc[i])))

    # Background
    fig.update_layout(plot_bgcolor= 'white')
    fig.update_xaxes(showline=True, linewidth=1, linecolor='Lightgray', mirror=True,
                     zeroline=True, zerolinewidth=1, zerolinecolor='Black',
                     showgrid=True, gridwidth=1, gridcolor='Lightgray', range =[-pad, 1+pad],
                     title = 'False Positive Rate (FPR)')
    fig.update_yaxes(showline=True, linewidth=1, linecolor='Lightgray', mirror=True,
                     zeroline=True, zerolinewidth=1, zerolinecolor='Black',
                     showgrid=True, gridwidth=1, gridcolor='Lightgray', range =[-pad, 1+pad],
                     title = 'True Positive Rate (TPR)')
    fig.update_yaxes(scaleanchor = "x", scaleratio = 1)
    fig.update_layout(height = 600, width = 810)
    fig.update_layout(title={'text': '<b>' + 'Receiver Operating Characteristic (ROC) Curves' + '<b>', 'x': .5,
                                         'y': .9, 'xanchor': 'center', 'yanchor': 'top'})
    fig.show()

pred_dicts = list(classifier.predict(input_fn=lambda: input_fn(X_test, y_test, training=False)))
clear_output()
probs = np.array([pred['probabilities'] for pred in pred_dicts])    
ROC_Curve(y_test, probs, n_classes = len(Labels_dict), FS = 8)

Confusion Matrix

The confusion matrix allows for visualization of the performance of an algorithm. Note that due to the size of data, here we don't provide a Cross-validation evaluation. In general, this type of evaluation is preferred.

def Confusion_Mat(CM_Train, CM_Test, PD, n_splits = 10):
    if n_splits == None:
        Titles = ['Train Set', 'Test Set']
    else:
        Titles = ['Train Set (CV = % i)' % n_splits, 'Test Set (CV = % i)' % n_splits]
    CM = [CM_Train, CM_Test]
    Cmap = ['Greens', 'YlGn','Blues', 'PuBu']
    for i in range(2):
        fig, ax = plt.subplots(1, 2, figsize= PD['FS'])
        fig.suptitle(Titles[i], weight = 'bold', fontsize = 16)
        _ = sns.heatmap(CM[i], annot=True, annot_kws={"size": PD['annot_kws']}, cmap=Cmap[2*i], ax = ax[0],
                        linewidths = 0.2, cbar_kws={"shrink": PD['shrink']})
        _ = ax[0].set_title('Confusion Matrix');
        Temp = np.round(CM[i].astype('float') / CM[i].sum(axis=1)[:, np.newaxis], 2)
        _ = sns.heatmap(Temp,
                        annot=True, annot_kws={"size": PD['annot_kws']}, cmap=Cmap[2*i+1], ax = ax[1],
                       linewidths = 0.4, vmin=0, vmax=1, cbar_kws={"shrink": PD['shrink']})
        _ = ax[1].set_title('Normalized Confusion Matrix');

        for a in ax:
            _ = a.set_xlabel('Predicted labels')
            _ = a.set_ylabel('True labels'); 
            _ = a.xaxis.set_ticklabels(PD['Labels'])
            _ = a.yaxis.set_ticklabels(PD['Labels'])
            _ = a.set_aspect(1)

# Train
pred_dicts = list(classifier.predict(input_fn=lambda: input_fn(X_train, y_train, training=False)))
clear_output()
probs = np.array([pred['probabilities'] for pred in pred_dicts])
y_pred = np.argmax(probs, axis = 1).reshape(-1,1)
Reports_Train = pd.DataFrame(metrics.classification_report(y_train, y_pred, target_names=list(Labels_dict.values()),
                                                           output_dict=True)).T
CM_Train = metrics.confusion_matrix(y_train, y_pred)
# Test
pred_dicts = list(classifier.predict(input_fn=lambda: input_fn(X_test, y_test, training=False)))
clear_output()
probs = np.array([pred['probabilities'] for pred in pred_dicts])
y_pred = np.argmax(probs, axis = 1).reshape(-1,1)
Reports_Test = pd.DataFrame(metrics.classification_report(y_test, y_pred, target_names=list(Labels_dict.values()),
                                                          output_dict=True)).T
CM_Test = metrics.confusion_matrix(y_test, y_pred)

Reports_Train = Reports_Train.reset_index().rename(columns ={'index': 'Train Set'})
Reports_Test = Reports_Test.reset_index().rename(columns ={'index': 'Test Set'})
                                                 
display(Reports_Train.style.hide_index().set_properties(**{'background-color': 'HoneyDew', 'color': 'Black'}).\
        set_properties(subset=['Train Set'], **{'background-color': 'SeaGreen', 'color': 'White'}))
display(Reports_Test.style.hide_index().set_properties(**{'background-color': 'Azure', 'color': 'Black'}).\
        set_properties(subset=['Test Set'], **{'background-color': 'RoyalBlue', 'color': 'White'}))

PD = dict(FS = (12, 6), annot_kws = 14, shrink = .6, Labels = list(Labels_dict.values()))
Confusion_Mat(CM_Train, CM_Test, PD = PD, n_splits = None)

Train Set	precision	recall	f1-score	support
Absent	1.000000	1.000000	1.000000	105.000000
Present	1.000000	1.000000	1.000000	84.000000
accuracy	1.000000	1.000000	1.000000	1.000000
macro avg	1.000000	1.000000	1.000000	189.000000
weighted avg	1.000000	1.000000	1.000000	189.000000

Test Set	precision	recall	f1-score	support
Absent	0.844444	0.844444	0.844444	45.000000
Present	0.805556	0.805556	0.805556	36.000000
accuracy	0.827160	0.827160	0.827160	0.827160
macro avg	0.825000	0.825000	0.825000	81.000000
weighted avg	0.827160	0.827160	0.827160	81.000000

Boosted Trees Classifier with $l_1$ regularization (Lasso)

Lasso (least absolute shrinkage and selection operator) classifier was introduced within the context of the method of least squares. Lasso) alters the model fitting process to pick only a subset of the provided covariates to be used within the final model instead of using all of them and this will improve the prediction accuracy and interpretability of regression models.

tf.keras.backend.clear_session()
IT = int(5e3)
# Classifier
classifier = tf.estimator.BoostedTreesClassifier(feature_columns=my_feature_columns,
                                                 n_batches_per_layer= 1,
                                                 n_classes= len(Labels_dict),
                                                 n_trees=120,
                                                 max_depth=5,
                                                 learning_rate=0.1,
                                                 l1_regularization= 1e-3)
# Training
classifier.train(input_fn=lambda: input_fn(X_train, y_train, training=True), max_steps = IT)
result = classifier.evaluate(input_fn=lambda: input_fn(X_test, y_test, training=False))
clear_output()
display(pd.DataFrame(result, index = ['']).round(4))

	accuracy	accuracy_baseline	auc	auc_precision_recall	average_loss	label/mean	loss	precision	prediction/mean	recall	global_step
	0.8519	0.5556	0.8932	0.8604	0.5694	0.4444	0.5694	0.8	0.4993	0.8889	600

ROC Curves

pred_dicts = list(classifier.predict(input_fn=lambda: input_fn(X_test, y_test, training=False)))
clear_output()
probs = np.array([pred['probabilities'] for pred in pred_dicts])    
ROC_Curve(y_test, probs, n_classes = len(Labels_dict), FS = 8)

Confusion Matrix

# Train
pred_dicts = list(classifier.predict(input_fn=lambda: input_fn(X_train, y_train, training=False)))
clear_output()
probs = np.array([pred['probabilities'] for pred in pred_dicts])
y_pred = np.argmax(probs, axis = 1).reshape(-1,1)
Reports_Train = pd.DataFrame(metrics.classification_report(y_train, y_pred, target_names=list(Labels_dict.values()),
                                                           output_dict=True)).T
CM_Train = metrics.confusion_matrix(y_train, y_pred)
# Test
pred_dicts = list(classifier.predict(input_fn=lambda: input_fn(X_test, y_test, training=False)))
clear_output()
probs = np.array([pred['probabilities'] for pred in pred_dicts])
y_pred = np.argmax(probs, axis = 1).reshape(-1,1)
Reports_Test = pd.DataFrame(metrics.classification_report(y_test, y_pred, target_names=list(Labels_dict.values()),
                                                          output_dict=True)).T
CM_Test = metrics.confusion_matrix(y_test, y_pred)

Reports_Train = Reports_Train.reset_index().rename(columns ={'index': 'Train Set'})
Reports_Test = Reports_Test.reset_index().rename(columns ={'index': 'Test Set'})
                                                 
display(Reports_Train.style.hide_index().set_properties(**{'background-color': 'HoneyDew', 'color': 'Black'}).\
        set_properties(subset=['Train Set'], **{'background-color': 'SeaGreen', 'color': 'White'}))
display(Reports_Test.style.hide_index().set_properties(**{'background-color': 'Azure', 'color': 'Black'}).\
        set_properties(subset=['Test Set'], **{'background-color': 'RoyalBlue', 'color': 'White'}))

PD = dict(FS = (12, 6), annot_kws = 14, shrink = .6, Labels = list(Labels_dict.values()))
Confusion_Mat(CM_Train, CM_Test, PD = PD, n_splits = None)

Train Set	precision	recall	f1-score	support
Absent	1.000000	1.000000	1.000000	105.000000
Present	1.000000	1.000000	1.000000	84.000000
accuracy	1.000000	1.000000	1.000000	1.000000
macro avg	1.000000	1.000000	1.000000	189.000000
weighted avg	1.000000	1.000000	1.000000	189.000000

Test Set	precision	recall	f1-score	support
Absent	0.902439	0.822222	0.860465	45.000000
Present	0.800000	0.888889	0.842105	36.000000
accuracy	0.851852	0.851852	0.851852	0.851852
macro avg	0.851220	0.855556	0.851285	81.000000
weighted avg	0.856911	0.851852	0.852305	81.000000

Boosted Trees Classifier with $l_2$ regularization (Ridge)

tf.keras.backend.clear_session()
IT = int(5e3)
# Classifier
classifier = tf.estimator.BoostedTreesClassifier(feature_columns=my_feature_columns,
                                                 n_batches_per_layer= 1,
                                                 n_classes= len(Labels_dict),
                                                 n_trees=120,
                                                 max_depth=5,
                                                 learning_rate=0.1,
                                                 l2_regularization= 1e-3)
# Training
classifier.train(input_fn=lambda: input_fn(X_train, y_train, training=True), max_steps = IT)
result = classifier.evaluate(input_fn=lambda: input_fn(X_test, y_test, training=False))
clear_output()
display(pd.DataFrame(result, index = ['']).round(4))

	accuracy	accuracy_baseline	auc	auc_precision_recall	average_loss	label/mean	loss	precision	prediction/mean	recall	global_step
	0.8765	0.5556	0.879	0.8448	0.691	0.4444	0.691	0.8421	0.474	0.8889	600

ROC Curves

pred_dicts = list(classifier.predict(input_fn=lambda: input_fn(X_test, y_test, training=False)))
clear_output()
probs = np.array([pred['probabilities'] for pred in pred_dicts])    
ROC_Curve(y_test, probs, n_classes = len(Labels_dict), FS = 8)

Confusion Matrix

# Train
pred_dicts = list(classifier.predict(input_fn=lambda: input_fn(X_train, y_train, training=False)))
clear_output()
probs = np.array([pred['probabilities'] for pred in pred_dicts])
y_pred = np.argmax(probs, axis = 1).reshape(-1,1)
Reports_Train = pd.DataFrame(metrics.classification_report(y_train, y_pred, target_names=list(Labels_dict.values()),
                                                           output_dict=True)).T
CM_Train = metrics.confusion_matrix(y_train, y_pred)
# Test
pred_dicts = list(classifier.predict(input_fn=lambda: input_fn(X_test, y_test, training=False)))
clear_output()
probs = np.array([pred['probabilities'] for pred in pred_dicts])
y_pred = np.argmax(probs, axis = 1).reshape(-1,1)
Reports_Test = pd.DataFrame(metrics.classification_report(y_test, y_pred, target_names=list(Labels_dict.values()),
                                                          output_dict=True)).T
CM_Test = metrics.confusion_matrix(y_test, y_pred)

Reports_Train = Reports_Train.reset_index().rename(columns ={'index': 'Train Set'})
Reports_Test = Reports_Test.reset_index().rename(columns ={'index': 'Test Set'})
                                                 
display(Reports_Train.style.hide_index().set_properties(**{'background-color': 'HoneyDew', 'color': 'Black'}).\
        set_properties(subset=['Train Set'], **{'background-color': 'SeaGreen', 'color': 'White'}))
display(Reports_Test.style.hide_index().set_properties(**{'background-color': 'Azure', 'color': 'Black'}).\
        set_properties(subset=['Test Set'], **{'background-color': 'RoyalBlue', 'color': 'White'}))

PD = dict(FS = (12, 6), annot_kws = 14, shrink = .6, Labels = list(Labels_dict.values()))
Confusion_Mat(CM_Train, CM_Test, PD = PD, n_splits = None)

Train Set	precision	recall	f1-score	support
Absent	1.000000	1.000000	1.000000	105.000000
Present	1.000000	1.000000	1.000000	84.000000
accuracy	1.000000	1.000000	1.000000	1.000000
macro avg	1.000000	1.000000	1.000000	189.000000
weighted avg	1.000000	1.000000	1.000000	189.000000

Test Set	precision	recall	f1-score	support
Absent	0.906977	0.866667	0.886364	45.000000
Present	0.842105	0.888889	0.864865	36.000000
accuracy	0.876543	0.876543	0.876543	0.876543
macro avg	0.874541	0.877778	0.875614	81.000000
weighted avg	0.878145	0.876543	0.876809	81.000000

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References

1. Regression analysis wikipedia page
2. Tensorflow tutorials
3. TensorFlow Boosted Trees Classifier
4. Lasso (statistics))
5. Tikhonov regularization
6. S. Aeberhard, D. Coomans and O. de Vel, Comparison of Classifiers in High Dimensional Settings, Tech. Rep. no. 92-02, (1992), Dept. of Computer Science and Dept. of Mathematics and Statistics, James Cook University of North Queensland. (Also submitted to Technometrics).
7. S. Aeberhard, D. Coomans and O. de Vel, “THE CLASSIFICATION PERFORMANCE OF RDA” Tech. Rep. no. 92-01, (1992), Dept. of Computer Science and Dept. of Mathematics and Statistics, James Cook University of North Queensland. (Also submitted to Journal of Chemometrics).

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